Suppose Sam has the opportunity for a treatment that will extend his life by one

Question

Suppose Sam has the opportunity for a treatment that will extend his life by one year with a probability of 0.62 by two years with a probability of 0.53, and three years with a probability of 0.25. Sam will die with certainty after three years. QALY weight q1 is 0.9 in year 1, q2 is 0.6 in year 2, and q3 is 0.2 in year 3. The discount rate is 7% per year. The total number of discounted QALYs from this treatment is:

I know the answer is 0.84 (rounded) and that it probably uses cost-benefit analysis, but I don't know how to get there.

Explanation / Answer

The discounted QALY in year 1 = probability * qaly weight * discount factor = 0.62 * 0.9* (1/1.07) = 0.521495

Discounted QALY in year 2 = 0.53 * 0.6 * (1/1.072) = 0.277754

Discounted QALY in year 3 = 0.25 * 0.2 * (1/1.073) = 0.040815

Total discounted QALY = 0.521495 + 0.277754 + 0.040815 = 0.840064 ~ 0.84

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